But there appears to be no evidence Yeats ever wrote it.
Yeats scholars on both sides of the Atlantic could find no trace of the often-quoted 14 words in databases that catalog writing produced by the poet, who was awarded the Nobel Prize in 1923.
Margaret Mills Harper, Glucksman Professor of Contemporary Writing in English at the University of Limerick in Ireland, searched for the line in a database of Yeats' published works, concordances to his poems and plays, and the electronic version of his complete letters.
"It's not in any of those places," she wrote in an email.
That was echoed by George Bornstein, a University of Michigan professor emeritus with an extensive list of publishing credits on Yeats and his poetry. He searched twice for the line in electronic records, without success.
"Maybe it is misattributed to Yeats," Bornstein suggested in an email, noting that similar sentiments on education were expressed by classical biographer Plutarch, among others.
Plutarch said, "The mind is not a vessel to be filled but a fire to be kindled," though that wording can vary in different translations.
The White House did not respond to a query about the source of the quotation
Brown credited the line to Yeats in a speech last week in Sacramento. His office pointed to online sources when asked about the validity of the quotation.
Yeats has been widely credited with the line used in speeches by politicians and educators, and even on a pillar at a North Carolina library.
Members of the W.B. Yeats Society of N.Y., an organization devoted to the poet's life and work, judged the quote of dubious authenticity after scouting Yeats writing and scholarship.
It's not uncommon for literary reputations to mingle with myth. Mark Twain was often credited with saying, "Whiskey is for drinking but water is worth fighting over," a remark also found to be of questionable legitimacy.
Yeats Society president Andrew McGowan said in a statement it was possible the education remark was "table talk" written down by someone else. "But the likelihood of that seemed weak," he said.
"This is like the line, 'A stranger is a friend we haven't met yet' that I'm told every Irish school child is taught Yeats said," McGowan added. "No evidence for it."